Page 72 - Aerodynamics for Engineering Students

Governing equations of fluid mechanics 55

Fig. 2.lb Aerofoil moves at speed V through air initially at rest. Axes Ox‘ Of fixed relative to
undisturbed air at rest

mathematical simplification mentioned earlier by eliminating time from the equations.
Since the flow relative to the air flow can, by a change of axes, be made steady, it is
sometimes known as ‘quasi-steady’.

True unsteady flow
An example of true unsteady flow is the wake behind a bluff body, e.g. a circular
cylinder (Fig. 2.2). The air is flowing from left to right, and the system of eddies or
vortices behind the cylinder is moving in the same direction at a somewhat lower
speed. This region of slower moving fluid is the ‘wake’. Consider a point P, fixed
relative to the cylinder, in the wake. Sometimes the point will be immersed in an eddy
and sometimes not. Thus the flow parameters will be changing rapidly at P, and the
flow there is unsteady. Moreover, it is impossible to find a set of axes relative to
which the flow is steady. At a point Q well outside the wake the fluctuations are so
small that they may be ignored and the flow at Q may, with little error, be regarded as
steady. Thus, even though the flow in some region may be unsteady, there may be
some other region where the unsteadiness is negligibly small, so that the flow there
may be regarded as steady with sufficient accuracy for all practical purposes.
Three concepts that are useful in describing fluid flows are:
(i) A streamline - defined as ‘an imaginary line drawn in the fluid such that there is
no flow across it at any point’, or alternatively as ‘a line that is always in the same

Fig. 2.2 True unsteady flow